namespace std {
template <intmax_t N, intmax_t D = 1> class ratio;
template <class R1, class R2> using ratio_add = see below;
template <class R1, class R2> using ratio_subtract = see below;
template <class R1, class R2> using ratio_multiply = see below;
template <class R1, class R2> using ratio_divide = see below;
template <class R1, class R2> struct ratio_equal;
template <class R1, class R2> struct ratio_not_equal;
template <class R1, class R2> struct ratio_less;
template <class R1, class R2> struct ratio_less_equal;
template <class R1, class R2> struct ratio_greater;
template <class R1, class R2> struct ratio_greater_equal;
template <class R1, class R2>
inline constexpr bool ratio_equal_v = ratio_equal<R1, R2>::value;
template <class R1, class R2>
inline constexpr bool ratio_not_equal_v = ratio_not_equal<R1, R2>::value;
template <class R1, class R2>
inline constexpr bool ratio_less_v = ratio_less<R1, R2>::value;
template <class R1, class R2>
inline constexpr bool ratio_less_equal_v = ratio_less_equal<R1, R2>::value;
template <class R1, class R2>
inline constexpr bool ratio_greater_v = ratio_greater<R1, R2>::value;
template <class R1, class R2>
inline constexpr bool ratio_greater_equal_v = ratio_greater_equal<R1, R2>::value;
using yocto = ratio<1, 1'000'000'000'000'000'000'000'000>; using zepto = ratio<1, 1'000'000'000'000'000'000'000>; using atto = ratio<1, 1'000'000'000'000'000'000>;
using femto = ratio<1, 1'000'000'000'000'000>;
using pico = ratio<1, 1'000'000'000'000>;
using nano = ratio<1, 1'000'000'000>;
using micro = ratio<1, 1'000'000>;
using milli = ratio<1, 1'000>;
using centi = ratio<1, 100>;
using deci = ratio<1, 10>;
using deca = ratio< 10, 1>;
using hecto = ratio< 100, 1>;
using kilo = ratio< 1'000, 1>;
using mega = ratio< 1'000'000, 1>;
using giga = ratio< 1'000'000'000, 1>;
using tera = ratio< 1'000'000'000'000, 1>;
using peta = ratio< 1'000'000'000'000'000, 1>;
using exa = ratio< 1'000'000'000'000'000'000, 1>;
using zetta = ratio< 1'000'000'000'000'000'000'000, 1>; using yotta = ratio<1'000'000'000'000'000'000'000'000, 1>; }
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